Post-pandemic economic recovery relies on border control for safe cross-border movement. Following the COVID-19 pandemic, we investigate whether effective strategies generalize across diseases and variants. For four SARS-CoV-2 variants and influenza A-H1N1, we simulated 21 strategy families of varying test types and frequencies, quantifying expected transmission risk, relative to no control, by strategy family and quarantine length. We also determined minimum quarantine lengths to suppress relative risk below given thresholds. SARS-CoV-2 variants showed similar relative risk across strategy families and quarantine lengths, with at most 2 days’ between-variant difference in minimum quarantine lengths. ART-based and PCR-based strategies showed comparable effectiveness, with regular testing strategies requiring at most 9 days. For influenza A-H1N1, ART-based strategies were ineffective. Daily ART testing reduced relative risk only 9% faster than without regular testing. PCR-based strategies were moderately effective, with daily PCR (0-day delay) testing requiring 16 days for the second-most stringent threshold. Viruses with high typical viral loads and low transmission risk given low viral loads, such as SARS-CoV-2, are effectively controlled with moderate-sensitivity tests (ARTs) and modest quarantine periods. Viruses with low typical viral loads and substantial transmission risk at low viral loads, such as influenza A-H1N1, require high-sensitivity tests (PCR) and longer quarantine periods.